Multivariate Nonnegative Quadratic Mappings
CentER Discussion Paper No. 2003-07
28 Pages Posted: 14 May 2004
Date Written: January 2003
In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a pre-specified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings de ned with respect to the positive semidefinite matrix cone, and study when it can be represented by linear matrix inequalities. We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models. In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semidefinite program.
Keywords: Linear Matrix Inequalities, Convex Cone, Robust Optimization, Bi-Quadratic Functions
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